## Trouble with the math

psyklopz
Posts: 2
Joined: Tue Apr 25, 2017 5:17 am

### Trouble with the math

Hi.

Finished reading the book. I'm having trouble with the most important equation in the book-- the one that tells you how long a retirement fund will last considering draw rate and interest rate.

As written in the book:
N = log[(1)/(1-(P)/(p)(i)/(1+i))]/log(1+i)

...where N is the number of years the fund will last
P is the initial fund size
p is the draw rate per year
i is the interest rate

If I plug in these numbers:
P = 10
p = 1
i = 0.04

...I can't get this to solve. Granted, my math isn't what it used to be.

This is what I am doing:

N = log[(1)/(1-(10)/(1)(0.04)/(1+0.04))]/log(1+0.04)
N = log[(1)/(1-(10)/(0.04)/(1.04))]/log(1.04)
N = log[(1)/(1-(250)/(1.04))]/log(1.04)
N = log[(1)/(1-(240.3846))]/log(1.04)
N = log[(1)/(-239.3846)]/log(1.04)
N = log[-0.004177]/log(1.04)

...and now we are in trouble because you can't take a log of a negative number.

I am certainly doing something wrong, I just don't know what it is.

Thanks in advance for the help!

jacob
Posts: 10827
Joined: Fri Jun 28, 2013 8:38 pm
Location: USA, Zone 5b, Koppen Dfa, Elev. 620ft, Walkscore 73
Contact:

### Re: Trouble with the math

So, we're talking about Eq. (7.10)

N = log[(1)/(1-(10)/(1)(0.04)/(1+0.04))]/log(1+0.04)
N = log[(1)/(1-(10)/(0.04)/(1.04))]/log(1.04)

going to

N = log[(1)/(1-(10)*0.03846)]/log(1.04)
N = log[1/(1-0.3846)]/log(1.04)

And so on ...

I don't know if you have the paperback or the kindle. The typesetting in the paperback is pretty clear whereas on kindle, it's all inline or one line. Generally here, one tries to resolve ambiguities with lots of parentheses. If such are lacking, the rule is generally that the / operator only touches the variable immediately following it, so ab/cd = ab/c * d and not ab/(cd). But yes .. this is an ancient problem and people will write ab/cd and mean ab/(cd) if it's "clear" that cd belongs together.

psyklopz
Posts: 2
Joined: Tue Apr 25, 2017 5:17 am

### Re: Trouble with the math

Yes, I have the kindle version. And yeah, lots of brackets But I can definitely understand the limitations of the format. I'll apply this rule and see if I can get it to work out.

Thanks!